Macroscopic Model for Head-On Binary Droplet Collisions in a Gaseous Medium.

Abstract

In this Letter, coalescence-bouncing transitions of head-on binary droplet collisions are predicted by a novel macroscopic model based entirely on fundamental laws of physics. By making use of the lubrication theory of Zhang and Law [Phys. Fluids 23, 042102 (2011)], we have modified the Navier-Stokes equations to accurately account for the rarefied nature of the interdroplet gas film. Through the disjoint pressure model, we have incorporated the intermolecular van der Waals forces. Our model does not use any adjustable (empirical) parameters. It therefore encompasses an extreme range of length scales (more than 5 orders of magnitude): from those of the external flow in excess of the droplet size (a few hundred μm) to the effective range of the van der Waals force around 10nm. A state of the art moving adaptive mesh method, capable of resolving all the relevant length scales, has been employed. Our numerical simulations are able to capture the coalescence-bouncing and bouncing-coalescence transitions that are observed as the collision intensity increases. The predicted transition Weber numbers for tetradecane and water droplet collisions at different pressures show good agreement with published experimental values. Our study also sheds new light on the roles of gas density, droplet size, and mean free path in the rupture of the gas film.